Formalization of Universal Algebra in Agda

In this work we present a novel formalization of universal algebra in Agda. We show that heterogeneous signatures can be elegantly modelled in type-theory using sets indexed by arities to represent operations. We prove elementary results of heterogeneous algebras, including the proof that the term algebra is initial and the proofs of the three isomorphism theorems. We further formalize equational theory and prove soundness and completeness. At the end, we define (derived) signature morphisms, from which we get the contravariant functor between algebras; moreover, we also proved that, under some restrictions, the translation of a theory induces a contra-variant functor between models.Fil: Gunther, Emmanuel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Gadea, Alejandro Emilio. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Pagano, Miguel Maria. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin

Monitoring-Oriented Programming: A Tool-Supported Methodology for Higher Quality Object-Oriented Software

This paper presents a tool-supported methodological paradigm for object-oriented software development, called monitoring-oriented programming and abbreviated MOP, in which runtime monitoring is a basic software design principle. The general idea underlying MOP is that software developers insert specifications in their code via annotations. Actual monitoring code is automatically synthesized from these annotations before compilation and integrated at appropriate places in the program, according to user-defined configuration attributes. This way, the specification is checked at runtime against the implementation. Moreover, violations and/or validations of specifications can trigger user-defined code at any points in the program, in particular recovery code, outputting or sending messages, or raising exceptions. The MOP paradigm does not promote or enforce any specific formalism to specify requirements: it allows the users to plug-in their favorite or domain-specific specification formalisms via logic plug-in modules. There are two major technical challenges that MOP supporting tools unavoidably face: monitor synthesis and monitor integration. The former is heavily dependent on the specification formalism and comes as part of the corresponding logic plug-in, while the latter is uniform for all specification formalisms and depends only on the target programming language. An experimental prototype tool, called Java-MOP, is also discussed, which currently supports most but not all of the desired MOP features. MOP aims at reducing the gap between formal specification and implementation, by integrating the two and allowing them together to form a system

Two Decades of Maude

This paper is a tribute to José Meseguer, from the rest of us in the Maude team, reviewing the past, the present, and the future of the language and system with which we have been working for around two decades under his leadership. After reviewing the origins and the language's main features, we present the latest additions to the language and some features currently under development. This paper is not an introduction to Maude, and some familiarity with it and with rewriting logic are indeed assumed.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Approaching Utopia: Strong Truthfulness and Externality-Resistant Mechanisms

We introduce and study strongly truthful mechanisms and their applications. We use strongly truthful mechanisms as a tool for implementation in undominated strategies for several problems,including the design of externality resistant auctions and a variant of multi-dimensional scheduling

A universe of processes and some of its guises

Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual foundations for this canvas, and how these can then be converted into mathematical structure. With very little structural effort (i.e. in very abstract terms) and in a very short time span the categorical quantum mechanics (CQM) research program has reproduced a surprisingly large fragment of quantum theory. It also provides new insights both in quantum foundations and in quantum information, and has even resulted in automated reasoning software called `quantomatic' which exploits the deductive power of CQM. In this paper we complement the available material by not requiring prior knowledge of category theory, and by pointing at connections to previous and current developments in the foundations of physics. This research program is also in close synergy with developments elsewhere, for example in representation theory, quantum algebra, knot theory, topological quantum field theory and several other areas.Comment: Invited chapter in: "Deep Beauty: Understanding the Quantum World through Mathematical Innovation", H. Halvorson, ed., Cambridge University Press, forthcoming. (as usual, many pictures